highfrequency (version 1.0.1)

HEAVYmodel: HEAVY model estimation

Description

This function calculates the High frEquency bAsed VolatilitY (HEAVY) model proposed in Shephard and Sheppard (2010).

Usage

HEAVYmodel(data, startingValues = NULL)

Value

The function outputs an object of class HEAVYmodel, a list containing

• coefficients = estimated coefficients.

• se = robust standard errors based on inverted Hessian matrix.

• residuals = the residuals in the return equation.

• llh = the two-component log-likelihood values.

• varCondVariances = conditional variances in the variance equation.

• RMCondVariances = conditional variances in the RM equation.

• data = the input data.

The class HEAVYmodel has the following methods: plot.HEAVYmodel, predict.HEAVYmodel, print.HEAVYmodel, and summary.HEAVYmodel.

Arguments

data

an xts object where the first column is a vector of returns and the second column is a vector of realized stock market variation

startingValues

a vector of alternative starting values: first three arguments for variance equation and last three arguments for measurement equation.

Author

Onno Kleen and Emil Sjorup.

Details

Let \(r_{t}\) and \(RM_{t}\) be series of demeaned returns and realized measures of daily stock price variation. The HEAVY model is a two-component model. We assume \(r_{t} = h_{t}^{1/2} Z_{t}\) where \(Z_t\) is an i.i.d. zero-mean and unit-variance innovation term. The dynamics of the HEAVY model are given by

$$ h_{t} = \omega + \alpha RM_{t-1} + \beta h_{t-1} $$ and $$ \mu_{t} = \omega_{R} + \alpha_{R} RM_{t-1} + \beta_{R} \mu_{t-1}. $$

The two equations are estimated separately as mentioned in Shephard and Sheppard (2010). We report robust standard errors based on the matrix-product of inverted Hessians and the outer product of gradients.

Note that we always demean the returns in the data input as we don't include a constant in the mean equation.

References

Shephard, N. and Sheppard, K. (2010). Realising the future: Forecasting with high frequency based volatility (HEAVY) models. Journal of Applied Econometrics 25, 197--231.

See Also

predict.HEAVYmodel

Examples

# Calculate returns in percentages
logReturns <- 100 * makeReturns(SPYRM$CLOSE)[-1]

# Combine both returns and realized measures into one xts
# Due to return calculation, the first observation is missing
dataSPY <- xts::xts(cbind(logReturns, SPYRM$BPV5[-1] * 10000), order.by = SPYRM$DT[-1])

# Fit the HEAVY model
fittedHEAVY <- HEAVYmodel(dataSPY)

# Examine the estimated coefficients and robust standard errors
fittedHEAVY

# Calculate iterative multi-step-ahead forecasts
predict(fittedHEAVY, stepsAhead = 12)